This disclosure relates generally to elastomeric couplings for transmitting torque between two shafts approximately aligned on a shaft axis, i.e., elastomeric couplings joining a pair of axially spaced shafts. The coupling has clamp rings with flange portions that are encapsulated in or embedded in and fixed in the material comprising the elastomeric element. The flange portions have a geometry which imparts a torsional stiffness characteristic of the coupling.